问题引领探究 演绎美妙课堂——《等比数列前n项和》教学实录与反思

《等比数列的前n项和公式》是苏教版普通高中数学课程标准实验教科书选修5第2.3.3节,主要内容是等比数列的前n项和公式的推导与应用.之前,学生学习了等差数列、等比数列的概念及通项公式,并掌握了等差数列前n项和公式的推导方法,具备了一定的探究能力.本节课的学习会促使学生产生思考：等比数列前n项和公式应该如何推导,公式应该从什么新的角度去建构.     

三维高斯拟合激光光强快速衰减算法

为缩短衰减倍率调整的时间,提高激光参数测试的效率,提出激光光强快速衰减算法。衰减倍率精确调整量由当前衰减倍率和采集到的光斑光强真实的最大灰度值共同决定。当因光电接收器件(CCD)饱和造成采集光斑图像失真时,即衰减倍率过小时,由于激光光斑的光强通常满足高斯分布,通过对光斑图像进行处理,去除饱和部分光强信息,对剩余部分光强信息利用最小二乘法进行三维高斯拟合,还原出激光光斑光强的真实分布并获得最大灰度值;当衰减倍率过大时,根据采集光斑图像可以直接获得当前最大灰度值,最后通过计算获得最佳的衰减倍率调整值,实现了激光光强快速准确的调整。算法的有效性通过步进电机带动的双轮可变衰减器及CCD配合得到验证。     

Electronic Phase Separation in Iron Selenide(Li,Fe)OHFeSe Superconductor System

The phenomenon of phase separation into antiferromagnetic(AFM) and superconducting(SC) or normal-state regions has great implication for the origin of high-temperature(high-T_c) superconductivity. However, the occurrence of an intrinsic antiferromagnetism above the T_c of(Li,Fe)OHFe Se superconductor is questioned. Here we report a systematic study on a series of(Li,Fe)OHFe Se single crystal samples with T_c up to ～41 K. We observe an evident drop in the static magnetization at T_(afm) ～ 125 K, in some of the SC(T_c 38 K, cell parameter c■9.27 ?) and non-SC samples. We verify that this AFM signal is intrinsic to(Li,Fe)OHFe Se. Thus, our observations indicate mesoscopic-to-macroscopic coexistence of an AFM state with the normal(below T_(afm)) or SC(below T_c) state in(Li,Fe)OHFe Se. We explain such coexistence by electronic phase separation, similar to that in high-T_c cuprates and iron arsenides. However, such an AFM signal can be absent in some other samples of(Li,Fe)OHFe Se, particularly it is never observed in the SC samples of T_c 38 K, owing to a spatial scale of the phase separation too small for the macroscopic magnetic probe. For this case, we propose a microscopic electronic phase separation. The occurrence of two-dimensional AFM spin fluctuations below nearly the same temperature as T_(afm), reported previously for a(Li,Fe)OHFe Se(T_c ～ 42 K) single crystal, suggests that the microscopic static phase separation reaches vanishing point in high T_c(Li,Fe)OHFe Se. A complete phase diagram is thus established. Our study provides key information of the underlying physics for high-T_c superconductivity.     

基于碳点的发光材料在潜在手印显现中的应用

遗留在犯罪现场的肉眼不可见的潜在手印是一类重要的痕迹物证,检验鉴定前需要使用一定技术手段将其显现出来。近年来,一些新材料和新技术的引入为手印显现技术的革新注入了新活力,其中稀土发光材料、量子点、荧光金属纳米簇等发光材料在该领域展现出极大潜力。碳点作为具有良好光致发光性能的新型纳米材料,近来逐渐引起了手印显现领域研究人员的广泛关注。本文综述了两类基于碳点材料的手印显现技术国内外研究进展,分别是液体分散碳点用于手印显现和固态发光碳点用于手印显现。具体来说,液体分散碳点显现手印的原理主要基于传统小微粒悬浮液机理或一些特殊效应(咖啡环效应、界面偏析效应);用于手印显现的固态发光碳点包括固态碳点粉末和固态碳点复合粉末两类,合成这些材料时研究人员采用了不同的策略。最后,从三个方面分析了碳点在手印显现应用中面临的问题,即碳点物理形貌和表面性质、碳点光致发光性质以及碳点显现过程与化学生物分析兼容性,并就解决问题的可能途径提出了展望。     

Yb3+,Er3+共掺BaGd2ZnO5材料的制备及其上转换发光效率

采用溶胶-凝胶法制备了含有不同Yb³⁺,Er³⁺掺杂浓度的BaGd₂ZnO₅上转换发光材料,测量了这些样品在不同激发光密度下的上转换光发射功率及上转换效率。实验结果表明:在不同激发光密度下,所有样品的光发射功率都存在极大值,其中Yb³⁺掺杂摩尔分数为4%,Er³⁺掺杂摩尔分数为1%时样品的最大发射光功率可达20 mW;样品的上转换绝对效率也存在极大值,随着Yb³⁺和Er³⁺浓度增加,绝对效率的极大值向较低激发光密度方向移动,在Yb³⁺掺杂摩尔分数为9%,Er³⁺掺杂摩尔分数为3%时样品的上转换效率达到最高,绝对效率为3.2%,极值效率最大值为6.9%。     

Controllable synthesis of high aspect ratio Mg_2B_2O_5 nanowires and their applications in reinforced polyhydroxyalkanoate composites

Highly pure magnesium borate （Mg2B2O5） nanowires with an average diameter of - 30 nm, an average length of 15 μm, and a high aspect ratio of - 500 have been synthesized on a large scale via a two-step method. MgBO2（OH） nanowires with high aspect ratios were first prepared via a PVP-assisted hydrothermal technique. Using these nanowires as precursors, single crystalline Mg2B205 nanowires were synthesized by post-annealing treatment at a relatively low temperature of 700 ℃. The important effect of the MgBO2（OH）-Mg2B2O5 conversion process on the morphology of the Mg2B2O5 nanowires was investigated and it was indicated that the recrystallization process plays an important role in the protection of the one-dimensional （1D） nanostructure. Moreover, the rigidity and the toughness of the Mg2B2O5 nanowire- reinforced PHA composites were tremendously improved compared to those of the pure PHA. Our results demonstrate the effectiveness of Mg2B2O5 nanowires for reinforcement applications in polymer composites.     

Effects of interface roughness on photoluminescence full width at half maximum in GaN/AlGaN quantum wells

Low temperature photoluminescence(PL) measurements have been performed for a set of GaN/AlxGa1-xN quantum wells(QWs). The experimental results show that the optical full width at half maximum(FWHM) increases relatively rapidly with increasing Al composition in the AlxGa1-xN barrier, and increases only slightly with increasing GaN well width. A model considering the interface roughness is used to interpret the experimental results. In the model, the FWHM’s broadening caused by the interface roughness is calculated based on the triangle potential well approximation. We find that the calculated results accord with the experimental results well.     

AlGaN合金中局域态和极化电场的竞争机制

通过MOVPE方法生长了不同Al组分的3块Al_xGa_1-xN样品,利用稳态光谱和时间分辨光谱对其样品的光学特性进行了分析。鉴于影响氮化物发光性质的极化电场或局域态的单一机制不能充分解释我们的实验现象,提出了局域态-内部极化电场竞争的机制。通过对实验数据的分析,得出如下重要结论：样品PL峰位蓝移的温度起点基本对应于局域态和极化电场起作用的交替点,PL峰位发生蓝移的温度起点与光强-温度曲线的斜率出现明显变化的温度点一致;随着温度的升高,若AlGaN合金样品中PL峰位存在二次蓝移,则说明样品中电场分布不均匀。     

炸药水中爆炸冲击因子的新型计算方法

针对水中爆炸冲击因子在近场范围内的一些不足,利用水中爆炸冲击波的最大峰值压力与正相冲量的乘积推导了冲击因子的表达式。通过水中爆炸实验,得到了几种典型炸药的冲击波参数及其相似方程。利用该公式计算了水中爆炸冲击因子及其装药指数,并与基于平面波的水下爆炸冲击因子进行了对比。结果表明:冲击因子中的装药指数n＝0.5不仅适合所有以TNT为基本组分的炸药,也适合于RDX、HMX基的炸药。在修正冲击波形状的基础上,由峰值压力与冲量的乘积推导的冲击因子计算公式,从冲击波的毁伤作用的角度表述了水中爆炸冲击因子的物理意义,在计算近场冲击因子时具有更高的准确性。     

聚合物刷水润滑条件下水膜厚度和摩擦学行为的相关性研究

利用表面引发原子转移自由基聚合技术(SI-ARTP)在钢球和玻璃盘摩擦副表面分别接枝亲水性聚合物刷-聚甲基丙烯酸-3-磺酸丙酯钾盐(PSPMA),去离子水作为润滑剂,在球-盘式摩擦试验机和纳米级薄膜厚度测量装置上开展了其宏观摩擦学性能研究,探讨了流体动压效应介入下的聚合物刷水润滑机理. 利用光干涉技术观察了低卷吸速度下(4 mm/s)接触区域水膜分布情况,发现滚道两侧水膜的形状由初始状态的圆形随着时间逐渐沿着卷吸方向分布,证实了聚合物刷通过不断捕获周围的水分子形成了1层稳定的水膜;通过控制卷吸速度从1 mm/s连续增加512 mm/s实现了润滑状态的转变,低卷吸速度时处于薄膜润滑状态,膜厚不依赖于速度且稳定在35 nm左右,接触区内有效水膜的建立归功于聚合物刷的水合效应;当速度大于32 mm/s时处于弹流润滑状态,膜厚的测量值高于等黏弹膜厚公式的预测值(2~12 nm)和水合效应促成的膜厚值(约35 nm)之和,这意味着在流体动压润滑作用下聚合物刷表现出了优异的润滑增强作用, 是水合效应和流体动压效应协同作用的结果.